Proportion / Ratio / Rate - PSAT Math
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A particular ball always bounces back to 2/5 of the height of its previous bounce after being dropped. After the first bounce it reaches a height of 175 inches. Approximately how high (in inches) will it reach after its fifth bounce?
A particular ball always bounces back to 2/5 of the height of its previous bounce after being dropped. After the first bounce it reaches a height of 175 inches. Approximately how high (in inches) will it reach after its fifth bounce?
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The first bounce reaches a height of 175. The second bounce will equal 175 multiplied by 2/5 or 70. Repeat this process. You will get the data below. 4.48 is rounded to 4.5.
The first bounce reaches a height of 175. The second bounce will equal 175 multiplied by 2/5 or 70. Repeat this process. You will get the data below. 4.48 is rounded to 4.5.
Alan is twice as old as Betty. He will be twice as old as Charlie in 10 years. If Charlie is 2 years old, how old is Betty?
Alan is twice as old as Betty. He will be twice as old as Charlie in 10 years. If Charlie is 2 years old, how old is Betty?
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If Charlie is 2 years old now; in 10 years he will be 12 years old. At that point, Alan will be twice as old as Charlie. Twice 12 is 24. This means that Alan is currently 10 years younger than 24, or 14. Since Alan is currently twice as old as Betty, she must be half of 14, or 7.
If Charlie is 2 years old now; in 10 years he will be 12 years old. At that point, Alan will be twice as old as Charlie. Twice 12 is 24. This means that Alan is currently 10 years younger than 24, or 14. Since Alan is currently twice as old as Betty, she must be half of 14, or 7.
The ratio of 10 to 14 is closest to what value?
The ratio of 10 to 14 is closest to what value?
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Another way to express ratios is through division. 10 divided by 14 is approximate 0.71.
Another way to express ratios is through division. 10 divided by 14 is approximate 0.71.
In 7 years Bill will be twice Amy’s age. Amy was 1.5 times Molly’s age 2 years ago. If Bill is 29 how old is Molly?
In 7 years Bill will be twice Amy’s age. Amy was 1.5 times Molly’s age 2 years ago. If Bill is 29 how old is Molly?
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Consider
(Bill + 7) = 2 x (Amy + 7)
(Amy – 2) = 1.5 x (Molly – 2)
Solve for Molly using the two equations by finding Amy’s age in terms of Molly’s age.
Amy = 2 + 1.5 Molly – 3 = 1.5 x Molly – 1
Substitute this into the first equation:
(Bill + 7) = 2 x (Amy + 7) = 2 x (1.5 x Molly – 1 + 7) = 2 x (1.5 x Molly + 6) = 3 x Molly + 12
Solve for Molly:
Bill + 7 – 12 = 3 x Molly
Molly = (Bill – 5) ¸ 3
Substitute Bill = 29
Molly = (Bill – 5) ¸ 3 = 8
Consider
(Bill + 7) = 2 x (Amy + 7)
(Amy – 2) = 1.5 x (Molly – 2)
Solve for Molly using the two equations by finding Amy’s age in terms of Molly’s age.
Amy = 2 + 1.5 Molly – 3 = 1.5 x Molly – 1
Substitute this into the first equation:
(Bill + 7) = 2 x (Amy + 7) = 2 x (1.5 x Molly – 1 + 7) = 2 x (1.5 x Molly + 6) = 3 x Molly + 12
Solve for Molly:
Bill + 7 – 12 = 3 x Molly
Molly = (Bill – 5) ¸ 3
Substitute Bill = 29
Molly = (Bill – 5) ¸ 3 = 8
In a mixture of flour and sugar, the ratio of flour to sugar is 5 to 1. How many kilograms of flour will there be in 12 kilograms of this mixture?
In a mixture of flour and sugar, the ratio of flour to sugar is 5 to 1. How many kilograms of flour will there be in 12 kilograms of this mixture?
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The question says that the mixture has 5 units of flour for every 1 unit of sugar, which adds up to a total of 5 + 1 = 6 units of the mixture; therefore in 6 kilograms of the mixture, 1 kilogram will be sugar.
To find how much sugar will be in 12 kilograms of the mixture, we multiply the amount of sugar in 6 kilograms of the mixture by 2, giving us 1 kilogram of sugar * 2 = 2 kilograms of sugar.
The question says that the mixture has 5 units of flour for every 1 unit of sugar, which adds up to a total of 5 + 1 = 6 units of the mixture; therefore in 6 kilograms of the mixture, 1 kilogram will be sugar.
To find how much sugar will be in 12 kilograms of the mixture, we multiply the amount of sugar in 6 kilograms of the mixture by 2, giving us 1 kilogram of sugar * 2 = 2 kilograms of sugar.
A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
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1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
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15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
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Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
If an object travels at 1200 ft per hour, how many minutes does it take to travel 180 ft?
If an object travels at 1200 ft per hour, how many minutes does it take to travel 180 ft?
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1200 ft per hour becomes 20 ft per second (divide 1200 by 60 because there are 60 minutes in an hour). 180/20 is 9, giving 9 minutes to travel 180 ft.
1200 ft per hour becomes 20 ft per second (divide 1200 by 60 because there are 60 minutes in an hour). 180/20 is 9, giving 9 minutes to travel 180 ft.
If you live 3 miles from your school. What average speed do you have to ride your bike get to your school from your house in 15 minutes?
If you live 3 miles from your school. What average speed do you have to ride your bike get to your school from your house in 15 minutes?
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The best way to find speed is to divide the distance by time. Since time is given in minutes we must convert minutes to hours so that our units match those in the answer choices. (3miles/15min)(60min/1hr)=12miles/hr; Remember when multipliying fractions to multiply straight across the top and bottom.
The best way to find speed is to divide the distance by time. Since time is given in minutes we must convert minutes to hours so that our units match those in the answer choices. (3miles/15min)(60min/1hr)=12miles/hr; Remember when multipliying fractions to multiply straight across the top and bottom.
If an airplane is flying 225mph about how long will it take the plane to go 600 miles?
If an airplane is flying 225mph about how long will it take the plane to go 600 miles?
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Speed = distance /time; So by solving for time we get time = distance /speed. So the equation for the answer is (600 miles)/ (225 miles/hr)= 2.67 hours; Remember to round up when the last digit of concern is 5 or more.
Speed = distance /time; So by solving for time we get time = distance /speed. So the equation for the answer is (600 miles)/ (225 miles/hr)= 2.67 hours; Remember to round up when the last digit of concern is 5 or more.
Vikki is able to complete 4 SAT reading questions in 6 minutes. At this rate, how many questions can she answer in 3 1/2 hours?
Vikki is able to complete 4 SAT reading questions in 6 minutes. At this rate, how many questions can she answer in 3 1/2 hours?
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First, find how many minutes are in 3 1/2 hours: 3 * 60 + 30 = 210 minutes. Then divide 210 by 6 to find how many six-minute intervals are in 210 minutes: 210/6 = 35. Since Vikki can complete 4 questions every 6 minutes, and there are 35 six-minute intervals we can multiply 4 by 35 to determine the total number of questions that she can complete.
4 * 35 = 140 problems.
First, find how many minutes are in 3 1/2 hours: 3 * 60 + 30 = 210 minutes. Then divide 210 by 6 to find how many six-minute intervals are in 210 minutes: 210/6 = 35. Since Vikki can complete 4 questions every 6 minutes, and there are 35 six-minute intervals we can multiply 4 by 35 to determine the total number of questions that she can complete.
4 * 35 = 140 problems.
The price of k kilograms of quartz is 50 dollars, and each kilogram makes s clocks. In terms of s and k, what is the price, in dollars, of the quartz required to make 1 clock?
The price of k kilograms of quartz is 50 dollars, and each kilogram makes s clocks. In terms of s and k, what is the price, in dollars, of the quartz required to make 1 clock?
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We want our result to have units of "dollars" in the numerator and units of "clocks" in the denominator. To do so, put the given information into conversion ratios that cause the units of "kilogram" to cancel out, as follows: (50 dollar/k kilogram)* (1 kilogram / s clock) = 50/(ks) dollar/clock.
Since the ratio has dollars in the numerator and clocks in the denominator, it represents the dollar price per clock.
We want our result to have units of "dollars" in the numerator and units of "clocks" in the denominator. To do so, put the given information into conversion ratios that cause the units of "kilogram" to cancel out, as follows: (50 dollar/k kilogram)* (1 kilogram / s clock) = 50/(ks) dollar/clock.
Since the ratio has dollars in the numerator and clocks in the denominator, it represents the dollar price per clock.
Minnie can run 5000 feet in 15 minutes. At this rate of speed, how long will it take her to fun 8500 feet?
Minnie can run 5000 feet in 15 minutes. At this rate of speed, how long will it take her to fun 8500 feet?
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Find the rate of speed. 5000ft/15 min = 333.33 ft per min
Divide distance by speed to find the time needed
8500ft/333.33ft per min = 25.5
Find the rate of speed. 5000ft/15 min = 333.33 ft per min
Divide distance by speed to find the time needed
8500ft/333.33ft per min = 25.5
1 meter contains 100 centimeters.
Find the ratio of 1 meter and 40 centimeters to 1 meter:
1 meter contains 100 centimeters.
Find the ratio of 1 meter and 40 centimeters to 1 meter:
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1m 40cm = 140cm. 1m = 100cm. So the ratio is 140cm:100cm. This can be put as a fraction 140/100 and then reduced to 14/10 and further to 7/5. This, in turn, can be rewritten as a ratio as 7:5.
1m 40cm = 140cm. 1m = 100cm. So the ratio is 140cm:100cm. This can be put as a fraction 140/100 and then reduced to 14/10 and further to 7/5. This, in turn, can be rewritten as a ratio as 7:5.
When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?
When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?
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One remote is defective for every 199 non-defective remotes.
One remote is defective for every 199 non-defective remotes.
If the ratio of q to r is 3:5 and the ratio of r to s is 10:7, what is the ratio of q to s?
If the ratio of q to r is 3:5 and the ratio of r to s is 10:7, what is the ratio of q to s?
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Multiply the ratios. (q/r)(r/s)= q/s. (3/5) * (10/7)= 6:7.
Multiply the ratios. (q/r)(r/s)= q/s. (3/5) * (10/7)= 6:7.
The first term in a sequence is m. If every term thereafter is 5 greater than 1/10 of the preceding term, and m≠0, what is the ratio of the second term to the first term?
The first term in a sequence is m. If every term thereafter is 5 greater than 1/10 of the preceding term, and m≠0, what is the ratio of the second term to the first term?
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The first term is m, so the second term is m/10+5 or (m+50)/10. When we take the ratio of the second term to the first term, we get (((m+50)/10))/m, which is ((m+50)/10)(1/m), or (m+50)/10m.
The first term is m, so the second term is m/10+5 or (m+50)/10. When we take the ratio of the second term to the first term, we get (((m+50)/10))/m, which is ((m+50)/10)(1/m), or (m+50)/10m.
Two cars were traveling 630 miles. Car A traveled an average speed of 70 miles per hour. If car B traveled 90 miles an hour, how many miles had car A traveled when car B arrived at the destination?
Two cars were traveling 630 miles. Car A traveled an average speed of 70 miles per hour. If car B traveled 90 miles an hour, how many miles had car A traveled when car B arrived at the destination?
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We first divide 630 miles by 90 miles per hour to get the amount of time it took car B to reach the destination, giving us 7 hours. We then multiply 7 hours by car A’s average speed and we get 490 miles.
We first divide 630 miles by 90 miles per hour to get the amount of time it took car B to reach the destination, giving us 7 hours. We then multiply 7 hours by car A’s average speed and we get 490 miles.
STUDENT ATHLETES WHO USE STEROIDS MEN WOMEN TOTAL BASKETBALL A B C SOCCER D E F TOTAL G H I
In the table above, each letter represents the number of students in each category. Which of the following must be equal to I?
| STUDENT ATHLETES WHO USE STEROIDS | |||
|---|---|---|---|
| MEN | WOMEN | TOTAL | |
| BASKETBALL | A | B | C |
| SOCCER | D | E | F |
| TOTAL | G | H | I |
In the table above, each letter represents the number of students in each category. Which of the following must be equal to I?
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Since G is the total number of male athletes that use steroids and H is the total number of female athletes that use steroids, the sum of the two is equal to I, which is the total number of all students using steroids.
Since G is the total number of male athletes that use steroids and H is the total number of female athletes that use steroids, the sum of the two is equal to I, which is the total number of all students using steroids.